the subgraph centrality of node \(v_i^\ell \) ; a relatively large value indicates that
this node is important because much information may pass through it. These notions of
communicability and subgraph centrality for nodes in multilayer graphs generalize the
analogous definitions introduced and explored by Estrada and his collaborators, as well as
others, in [1]}, [2]}, [3]}, [4]}, [5]} for single-layer networks. In these references \(\mathcal {A}\) 
in (REF ) is replaced by the adjacency matrix for the single-layer graph and,
hence, \(f\)  is a matrix function.
